A wire of `9.8xx10^(-3) kg/m` passes over a frictionless light pulley fixed on the top of a frictionless inclined plane which makes an angle of `30^(@)` with the horizontal. Masses m and M are tied at the two ends of wire such that m rests on the plane and M hangs freely vertically downwards. the entire system is in equilibrium and a transverse wave propagates along the wire with a velocities of `100 m//s`.

Options

A. `m=20 kg`
B. `M=5 kg`
C. `(m)/(M)=(1)/(2)`
D. `(m)/(M)=2`

Answer

a., d.

Explanation

`v=sqrt((T)/(mu))`
For equilibrium `Mg=mg sin 30=T`
`M=m//2`
`100=sqrt((Mg)/(9.8xx10^(-3)))=sqrt((M(9.8))/(9.8xx10^(-3))`
`100=sqrt(M(1000))`
`M=10 kg and m=20 kg`